Related papers: Some generalized numerical radius inequalities inv…

We establish the following Hadamard--Stoker type theorem: Let $f:M^n\rightarrow\mathscr{H}^n\times\mathbb R$ be a complete connected hypersurface with positive definite second fundamental form, where $\mathscr H^n$ is a Hadamard manifold.…

We establish the membership criteria in terms of Hadamard product for a normalized analytic function to be in the class of infinitesimal generators. Furthermore, the embedding of various subclasses of normalized univalent functions in the…

To every subspace arrangement X we will associate symmetric functions P[X] and H[X]. These symmetric functions encode the Hilbert series and the minimal projective resolution of the product ideal associated to the subspace arrangement. They…

Let $F_{BC}(\lambda,k;t)$ be the Heckman-Opdam hypergeometric function of type BC with multiplicities $k=(k_1,k_2,k_3)$ and weighted half sum $\rho(k)$ of positive roots. We prove that $F_{BC}(\lambda+\rho(k),k;t)$ converges for…

We use the remark that, through Bargmann-Fock representation, diagonal operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product to give some properties (like the stability of periodic fonctions) of the Hadamard product…

Inequalities among symmetric polynomial functions are fundamental questions in mathematics and have various applications in science and engineering. This paper investigates a beautiful and inspiring conjecture, proposed by Cuttler, Greene…

For real symmetric positive definite matrices $A$ and $B$, we characterize when a function $f \in L^2(\mathbb{R}^d)$ satisfies \[ |f(x)| \lesssim e^{-(\frac12 - \lambda) \langle Ax, x\rangle} \quad \text{and} \quad |\widehat{f}(\xi)|…

We establish the full range of the Caffarelli-Kohn-Nirenberg inequalities for radial functions in the Sobolev and the fractional Sobolev spaces of order $0 < s \le 1$. In particular, we show that the range of the parameters for radial…

It is shown that, for any function $g$ that is weakly increasing on compact convex sets and has the property that if $\lambda\ge 0$ and $K^\prime$ is a translate of $\lambda K$ then $g(K^\prime) =\lambda g(K)$, then for any covering…

The main objective of present investigation to obtain some Minkowski-type fractional integral inequalities using generalised proportional Hadamard fractional integral operators which is introduced by Rahman et al in the paper (certain…

Let $X$ be a Banach space, let $(\Omega,\mu)$ be a $\sigma$-finite measure space and let $A,B\colon\Omega\to B(X)$ be strongly measurable $\gamma$-bounded functions. We show that for all $x\in X$ and all $x^*\in X^*$, there exist a Hilbert…

Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…

By a result of Lundquist-Barrett, it follows that the rank of a positive semi-definite matrix is less than or equal to the sum of the ranks of its principal diagonal submatrices when written in block form. In this article, we take a general…

We will show that if $\sM$ is a factor, then for any pair $\f, \p\in\sMdsup$ of normal positive linear functionals on $\sM$, the inequality: $$ \lrnorm{\f}\leq \lrnorm{\p} $$ is equivalent to the fact that there exist a countable family…

In this paper, we establish some Hadamard-type inequalities based on coordinated quasi-convexity. Also we define a new mapping associated to coordinated convexity and we prove some properties of this mapping.

In this paper, we establish some new Hadamard type inequalities for s-logarithmically convex functions in the second sense via fractional integrals by using Lemma 1 which has been proved by Sarikaya et al. in the paper [3].

In this paper several inequalities of the right-hand side of Hermite-Hadamard's inequality are obtained for the class of functions whose derivatives in absolutely value at certain powers are strongly {\varphi}-convex with modulus c>0.

We find sufficient conditions for log-convexity and log-concavity for the functions of the forms $a\mapsto\sum{f_k}(a)_kx^k$, $a\mapsto\sum{f_k}\Gamma(a+k)x^k$ and $a\mapsto\sum{f_k}x^k/(a)_k$. The most useful examples of such functions are…

A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a…

We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on matrices. We then utilize the Mond-Pecaric method to get an operator version for convex…